From Eq. (REF ), the expectation value at the simulation point \((\beta , \kappa )\)  can be expressed in terms of those at a different simulation point \((\beta _0, \kappa _0)\)  by the reweighting method [1]}:
\(\langle {\cal O} \rangle _{(\beta , \kappa )}= \frac{ \langle {\cal O} \,[\det M(\kappa )/ \det M(\kappa _0)]^{N_{\rm f}} \, e^{6 (\beta - \beta _0) N_{\rm site} \hat{P}} \rangle _{(\beta _0, \kappa _0)} }{\langle [\det M(\kappa )/ \det M(\kappa _0)]^{N_{\rm f}} \, e^{6 (\beta - \beta _0) N_{\rm site} \hat{P}} \rangle _{(\beta _0, \kappa _0)} }.\) 
